Time–frequency characteristic analysis method for track geometry irregularities based on multivariate empirical mode decomposition and Hilbert spectral analysis
Youtao Yang, Guoxiang Liu, Xiaowen Wang
Abstract
The description and evaluation of track geometry irregularities are commonly performed in the distance domain or the frequency domain, and therefore one cannot simultaneously obtain precise measurements of actual frequencies and the distance locations where they appear. This paper proposes the time–frequency energy density (TFED) method to analyse the characteristics of track irregularities in the joint spatial distance–frequency plane. The proposed method describes the energy density distribution of track irregularities in the spatial distance–frequency domain based on the adaptive decomposition characteristics of the multivariate empirical mode decomposition and the time–frequency aggregation on the signal energy of the Hilbert spectrum. The mathematical relationships between the TFED and the standard deviation, as well as the power spectral density, are deduced and validated in the field data of track irregularities. The TFED method was applied to the spatial distance–frequency characteristic distribution of track irregularities and the distribution of instantaneous energy density in the sensitive wavelengths. The track geometry quality is evaluated based on the TFED, using track inspection data of actual high-speed railways.